{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:P6GQCH5LVHYK3ZMAIISEDAB4XV","short_pith_number":"pith:P6GQCH5L","canonical_record":{"source":{"id":"2606.04950","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-03T14:39:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d07e92ec489be703f1ad2d63e24b9f991a463818ec9c67c72c8e6cf9601dda53","abstract_canon_sha256":"d128013c314a6b0b7ee5b03dce51f225717e761571693506297e5b8db6789c96"},"schema_version":"1.0"},"canonical_sha256":"7f8d011faba9f0ade580422441803cbd5871d399745260d6c8a1394e9c2a3c3d","source":{"kind":"arxiv","id":"2606.04950","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04950","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04950v1","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04950","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"P6GQCH5LVHYK","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"pith_short_16","alias_value":"P6GQCH5LVHYK3ZMA","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"pith_short_8","alias_value":"P6GQCH5L","created_at":"2026-06-04T01:09:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:P6GQCH5LVHYK3ZMAIISEDAB4XV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.04950","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-03T14:39:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d07e92ec489be703f1ad2d63e24b9f991a463818ec9c67c72c8e6cf9601dda53","abstract_canon_sha256":"d128013c314a6b0b7ee5b03dce51f225717e761571693506297e5b8db6789c96"},"schema_version":"1.0"},"canonical_sha256":"7f8d011faba9f0ade580422441803cbd5871d399745260d6c8a1394e9c2a3c3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:57.602041Z","signature_b64":"2n7bKTX5rjm1sQA7WZASl5x2Vc/HRgFK4uarEVMc3w/0kZ9OWXZs+pcqUKLgEWPyeZS+jUfDrrBnlyJI48T+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f8d011faba9f0ade580422441803cbd5871d399745260d6c8a1394e9c2a3c3d","last_reissued_at":"2026-06-04T01:09:57.601259Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:57.601259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.04950","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NvQPOxNS3aFshe1kO6nHOjuXpAWQE1HckDkLoWLEVI1c3weVibntBmx+M4cbqe3mUMdpt3cqedQbT+BPE1tUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:53:13.394923Z"},"content_sha256":"68cf57f88f59706998ba2a28e954687c159c6d4c22a865ae1b6eaf8c3fa27c38","schema_version":"1.0","event_id":"sha256:68cf57f88f59706998ba2a28e954687c159c6d4c22a865ae1b6eaf8c3fa27c38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:P6GQCH5LVHYK3ZMAIISEDAB4XV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Tricomi equation in the hyperbolic half plane under additive space-time Gaussian White Noise perturbation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Alberto Lanconelli, Enrico Bernardi","submitted_at":"2026-06-03T14:39:15Z","abstract_excerpt":"We study the Cauchy problem for the Tricomi equation perturbed by space-time Gaussian White Noise. To prove existence and uniqueness of the solution, we employ a Fourier transform approach that allows to obtain its representation in terms of certain integrals of the Airy functions. Then, via a careful analysis of the asymptotic behaviour of those integrals, we obtain all the desired properties of the solution, such as square integrability, continuity of its sample paths and stationarity with respect to the space variable. In relation to that stationarity, we also provide the precise descriptio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04950","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04950/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kUZziXwHamxBraPhn5t6QrbIJKRkWU3dx9faNJ1dy10xOEhJu9i9gxAnRMN6sMwdGi8GWBOahQ9QTZpDPzSsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:53:13.395299Z"},"content_sha256":"e60261d99473ca097fb9cc83036caadb7e2d4aa01ea01b55764452c9acb6853d","schema_version":"1.0","event_id":"sha256:e60261d99473ca097fb9cc83036caadb7e2d4aa01ea01b55764452c9acb6853d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6GQCH5LVHYK3ZMAIISEDAB4XV/bundle.json","state_url":"https://pith.science/pith/P6GQCH5LVHYK3ZMAIISEDAB4XV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6GQCH5LVHYK3ZMAIISEDAB4XV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T04:53:13Z","links":{"resolver":"https://pith.science/pith/P6GQCH5LVHYK3ZMAIISEDAB4XV","bundle":"https://pith.science/pith/P6GQCH5LVHYK3ZMAIISEDAB4XV/bundle.json","state":"https://pith.science/pith/P6GQCH5LVHYK3ZMAIISEDAB4XV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6GQCH5LVHYK3ZMAIISEDAB4XV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P6GQCH5LVHYK3ZMAIISEDAB4XV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d128013c314a6b0b7ee5b03dce51f225717e761571693506297e5b8db6789c96","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-03T14:39:15Z","title_canon_sha256":"d07e92ec489be703f1ad2d63e24b9f991a463818ec9c67c72c8e6cf9601dda53"},"schema_version":"1.0","source":{"id":"2606.04950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04950","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04950v1","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04950","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"P6GQCH5LVHYK","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"pith_short_16","alias_value":"P6GQCH5LVHYK3ZMA","created_at":"2026-06-04T01:09:57Z"},{"alias_kind":"pith_short_8","alias_value":"P6GQCH5L","created_at":"2026-06-04T01:09:57Z"}],"graph_snapshots":[{"event_id":"sha256:e60261d99473ca097fb9cc83036caadb7e2d4aa01ea01b55764452c9acb6853d","target":"graph","created_at":"2026-06-04T01:09:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.04950/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Cauchy problem for the Tricomi equation perturbed by space-time Gaussian White Noise. To prove existence and uniqueness of the solution, we employ a Fourier transform approach that allows to obtain its representation in terms of certain integrals of the Airy functions. Then, via a careful analysis of the asymptotic behaviour of those integrals, we obtain all the desired properties of the solution, such as square integrability, continuity of its sample paths and stationarity with respect to the space variable. In relation to that stationarity, we also provide the precise descriptio","authors_text":"Alberto Lanconelli, Enrico Bernardi","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-03T14:39:15Z","title":"The Tricomi equation in the hyperbolic half plane under additive space-time Gaussian White Noise perturbation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04950","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:68cf57f88f59706998ba2a28e954687c159c6d4c22a865ae1b6eaf8c3fa27c38","target":"record","created_at":"2026-06-04T01:09:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d128013c314a6b0b7ee5b03dce51f225717e761571693506297e5b8db6789c96","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-03T14:39:15Z","title_canon_sha256":"d07e92ec489be703f1ad2d63e24b9f991a463818ec9c67c72c8e6cf9601dda53"},"schema_version":"1.0","source":{"id":"2606.04950","kind":"arxiv","version":1}},"canonical_sha256":"7f8d011faba9f0ade580422441803cbd5871d399745260d6c8a1394e9c2a3c3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f8d011faba9f0ade580422441803cbd5871d399745260d6c8a1394e9c2a3c3d","first_computed_at":"2026-06-04T01:09:57.601259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:57.601259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2n7bKTX5rjm1sQA7WZASl5x2Vc/HRgFK4uarEVMc3w/0kZ9OWXZs+pcqUKLgEWPyeZS+jUfDrrBnlyJI48T+Bw==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:57.602041Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68cf57f88f59706998ba2a28e954687c159c6d4c22a865ae1b6eaf8c3fa27c38","sha256:e60261d99473ca097fb9cc83036caadb7e2d4aa01ea01b55764452c9acb6853d"],"state_sha256":"7ce0a6c168bd9400155cfdd555a09dc432dbb4aac6640742f655475a29e4217c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8VgAi3B2CifXfrMK0e9jjyzmMPuC2YYmda0hrtFWkBbgurxuhaUJp0rd1TXGELzz3AI41pwrq+Kfwo+ixi6tAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:53:13.397391Z","bundle_sha256":"281159f134d767866e11ddb9284bc9e287f8a0f37b102e016edc28b2acafb77e"}}